Answer to Question #291350 in Real Analysis for Nikhil Singh

Question

Sketch the graph of the function, f defined by

f(x)= |x-3| +[x], x∈ [2,4] where [x] denotes the greatest integer function

Answer 1

$$f(x) = \begin{cases} 3-x+2, &2\leq x<3 \\ x-3+3, &3\leq x<4 \\ x-3+4, &x=4 \end{cases}$$

$$f(x) = \begin{cases} 5-x, &2\leq x<3 \\ x, &3\leq x<4 \\ 5, &x=4 \end{cases}$$